A new method for bending problems of nonlinear viscoelastic beam

In this paper, firstly, based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for bending problems of nonlinear viscoelastic beams is set up. Secondly, the Laplace transformation method is used to prove that some relations exist between solutions for bending problems of viscoelastic and elastic beams. The corresponding relations provide a new method for solving viscoelastic problems. Part of responses of viscoelastic problems could be obtained directly from the corresponding elastic ones by these relations. Compared with the traditional finite difference method in the time domain, the computational time is greatly shortened.